rfl-urbaniak
commented
2 months ago read through, here are some comments, then we can discuss the points Marcello brought up:
p.1
independent (ยง6 and 7).
add par symbol
p. 4
fn 7 lacks a stop period; perhaps also consider something about why we don't think this is a great option.
p. 5
can be evaluated
to
can, perhaps, be evaluated
p. 6
a probability density to each proposition of interest
to
a probability density or a probability mass function over a (potentially discretized for computational ease) space of probabilities of each first-order proposition of interest whose probabilities they don't want to estimate or approximate using precise values
p 6
usually defined as
to
defined as
p 6
1000 first-order probabilities
move the remark to fn, and expand into
1000 first-order probabilities -- then, we can get away with using a probability mass function for this discretized space; also, for the sake of simplicity, throughout, we will not consider dependencies between probabilities of different propositions, and not use multivariate distributions over the parameter space)
p 8
be limited to first-order ones.
be limited to the first-order ones.
p. 8
Instead, X2 -precie probabilism
precise
p. 8
and second-order propositions as ad hoc postulates.
...as separate postulates, instead of having them fall out from rather straightforward Bayesian principles
p. 8
What's the point of fn 16? Seems like we pick a view without giving any citation for it and say nothing about it.
p. 9 is a natural starting point.
to
is a natural starting point already present in the literature [CITE KONEK]
p 12
for any other probability distribution ๐ different from ๐
to
for any probability distribution ๐ different from ๐
higher-order probability distributions of different coincidental match probabilities given the sample data
to
...the sample data, assuming the expert started with uniform priors
Description of Figure 8:
Figure 8: Impact of incoming evidence in the Sally Clark case.
to
I revised the higher order probabilism paper revised up to section 4 only. I incorporated most of Rafal's replies in #95 to the reviewers:
Please check whether the revisions are acceptable. (File is in ru-imprecision-paper-rmd branch branch, file name is imp_philosophical_agust2024.qmd)
Before moving forward, I need clarifications about a few points, see below:
Defintion of higher-order probabilism. In the new version, HOP is defined as follows: a mapping from a set of first-order propositions to probability densities, so each proposition of interest is assigned (not a single probability value) but a probability density. I ma not sure about this framing. Is this right?
This is different from what we might call higher-order (precise) probabilism, that is, a mapping from a set of propositions (some including propositions about probabilities) to precise probability values between 0 and 1.
Higher-order match probabilities: If higher-order probabilism is defined as above, then what are we talking about in section 6 when we discuss higher-order match probabilities? What proposition is associated to what density in this case? Looks like we are assigning probabilities to P(match|innocence)=x, just like higher-order (precise) probabilism would recommend. This is confusing because it does not match up our earlier defintion of higher-order probabilism. So something is off and might expalain also the reviwere hesitation.
Densities versus distributions. I am still unclear how we use densities versus distributions in the paper. We use densities up to section 4 and then in 5 and 6 switch to distributions and almost never talk about densities again. Thus is confusing to me. The switch is not motivated. In section 6 we use densities in the caption of the figures but distributions in the text. Seems very sloppy unless there is something I am missing.
The paper is currently too long if we want to submit it to Australasian JP with a has 8,000 word limit. We could cut out the section about higher-order proper scores, give a brief proof in the appendix and remove the long discussion about the coin example. This should bring us down closer to the limit, along with some other surgical cuts in other sections. I've already made cuts in section 1, 2, 3 and 4 and footnotes.
see also my discussion in issue #96, especially discussion of pearl paper